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 A211561 T(n,k) = number of nonnegative integer arrays of length n+k-1 with new values 0 upwards introduced in order, and containing the value k-1. 12
 1, 1, 2, 1, 4, 5, 1, 7, 14, 15, 1, 11, 36, 51, 52, 1, 16, 81, 171, 202, 203, 1, 22, 162, 512, 813, 876, 877, 1, 29, 295, 1345, 3046, 4012, 4139, 4140, 1, 37, 499, 3145, 10096, 17866, 20891, 21146, 21147, 1, 46, 796, 6676, 29503, 72028, 106133, 115463, 115974, 115975 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ....1.....1......1......1.......1........1........1.........1..........1 ....2.....4......7.....11......16.......22.......29........37.........46 ....5....14.....36.....81.....162......295......499.......796.......1211 ...15....51....171....512....1345.....3145.....6676.....13091......24047 ...52...202....813...3046...10096....29503....77078....183074.....401337 ..203...876...4012..17866...72028...256565...810470...2300949....5957407 ..877..4139..20891.106133..503295..2134122..8016373..26869727...81381744 .4140.21146.115463.649045.3513522.17337685.76199007.298009584.1046405027 Reading along antidiagonals seems to create A137650. - R. J. Mathar, Nov 29 2015 See also A133611. - Alois P. Heinz, Aug 30 2019 LINKS R. H. Hardin, Table of n, a(n) for n = 1..9999 FORMULA Empirical: T(n,k) = Sum_{j=k..n+k-1} stirling2(n+k-1,j) EXAMPLE Some solutions for n=5, k=4: ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 ..1....1....1....0....1....1....1....1....0....1....1....1....1....1....1....0 ..1....2....2....0....0....2....2....0....1....2....2....2....2....0....2....1 ..2....0....2....0....2....0....3....2....2....2....3....3....2....2....0....2 ..3....1....3....1....3....2....1....3....3....2....1....3....3....2....1....2 ..4....0....3....0....3....3....4....1....3....3....0....2....4....3....2....2 ..5....3....3....2....4....4....2....1....2....2....1....0....4....3....3....2 ..2....0....1....3....5....4....4....4....4....2....0....4....3....1....2....3 CROSSREFS Column 1 is A000110. Column 2 is A058692(n+1). Column 3 is A058681(n+1). Row 2 is A000124. Cf. A133611, A137650. Sequence in context: A371686 A321000 A121289 * A134248 A248670 A080935 Adjacent sequences: A211558 A211559 A211560 * A211562 A211563 A211564 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Apr 15 2012 STATUS approved

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Last modified May 19 07:05 EDT 2024. Contains 372666 sequences. (Running on oeis4.)